Thread: exponentail

On January 8, 10 students come down with the flu. Assume that each day, the number of students who come down with the flu doubles. So, for example, 20 students come down with the flu on Jan. 9. Let f(t) represent the number fo students who come down with the flu at t days since Jan.8.

a) Find an equation for f
Hopefully this is right f(t)=10(2)^t

b)Find f(7). What does your result mean in terms of the situation?

f(t)=10(2)^7
1280 In 7 days since January 8 which will be January 15, 1280 students will have the flu.

Originally Posted by getnaphd

On January 8, 10 students come down with the flu. Assume that each day, the number of students who come down with the flu doubles. So, for example, 20 students come down with the flu on Jan. 9. Let f(t) represent the number fo students who come down with the flu at t days since Jan.8.

a) Find an equation for f
Hopefully this is right f(t)=10(2)^t

correct

b)Find f(7). What does your result mean in terms of the situation?

f(t)=10(2)^7
1280 In 7 days since January 8 which will be January 15, 1280 students will have the flu.

again, correct

however you should write f(7) = 10(2)^7 = 1280, not f(t), f(t) is 10(2)^t

and what do you need help with agian?

you've already answered the questions save for "what does this mean?"

and that's something you need to say in your own words.

Alright.

Thanks for correcting .

Here is another problem which I think I solved. Could you make sure I am on the right track?

An archeologist discovers a tool made of wood.

a. If 50% of the wood's carbon-14 remains, how old is the wood? Explain how you can find this result without using an equation. Recall that the half life of carbon-14 is 5730 years.

My answer: The answer is 5730 because 50% is half of the whole life 100%

b. If 25% of the woods carbon remains, how old is the wood? Explain how you can find this result without using an equation?

My answer: I would take half of the 5730 =2865 and then add it to the original 5730 to get 8595

c. If 10% of the woods carbon-14 remains, how old is the wood? First guess an approximate age without solving an equation. Explain how you decided on your estimate. Then, use an equation to find the result.

My answer is to take 10% of 5730 and add it to 8595?

For some reason I am now stuck.

Please post new questions in a new thread.

Originally Posted by getnaphd

An archeologist discovers a tool made of wood.

a. If 50% of the wood's carbon-14 remains, how old is the wood? Explain how you can find this result without using an equation. Recall that the half life of carbon-14 is 5730 years.

My answer: The answer is 5730 because 50% is half of the whole life 100%

correct

b. If 25% of the woods carbon remains, how old is the wood? Explain how you can find this result without using an equation?

My answer: I would take half of the 5730 =2865 and then add it to the original 5730 to get 8595

incorrect

25% is half of 50%, so it will take another half life to get to 25% (the half life is the time it takes for 1/2 of whatever is left to decay).

so the answer is 2*half-life = 11460 years

c. If 10% of the woods carbon-14 remains, how old is the wood? First guess an approximate age without solving an equation. Explain how you decided on your estimate. Then, use an equation to find the result.

My answer is to take 10% of 5730 and add it to 8595?

10% is roughly a half of 25% so my original estimate would be around another half life added to the previous one.

so, original estimate: 3*half-life = 17190 years

however, in actuality, it would take that long to get to 12.5%, so we need a little extra time to get to 10%

10% is 80% of 12.5%, so 20% more has decayed. 20% is roughly half of 50%, so i expect it would take just over (1/2)*half life more to get there = 20055 years, roughly